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We give a complete classification of finite-dimensional simple Novikov algebras and their irreducible modules over an algebraically closed field with prime characteristic. Moreover, we introduce ''Novikov᎐Poisson algebras'' and their tensor theory. Our tensor theory enables us to understand better certain finite-dimensional simple Novikov algebras and their irreducible modules. ᮊ 1996 Academic Press, Inc.

A series of amine bis(phenolato)lanthanide methyl and amido complexes were synthesized by general salt metathesis reaction in this paper. The reaction of anhydrous lanthanide trichlorides with 1 equiv of sodium amine bis(phenolatein THF at room temperature gave the amine bis(phenolate) lanthanide chlorides LLnCl(THF) (Ln ) Yb (1), Ln ) Er ( 2)). Complexes 1 and 2 can be used as starting materials to prepare amine bis(phenolate) lanthanide derivatives. Complexes 1 and 2 reacted with lithium methyl and lithium amide, respectively, to give the corresponding lanthanide methyl and amido products LLnMe(THF) (Ln ) Yb (3), Ln ) Er ( 4)) and LLnNPh 2 (THF) (Ln ) Yb (5), Ln ) Er ( 6)). These complexes were well characterized by elemental analyses and IR spectra. The definitive molecular structures of complexes 1, 2, 3, 5, and 6 were provided by single-crystal X-ray analyses. Reactivity studies of complexes 3, 5, and 6 have shown them to be efficient initiators for the ring-opening polymerization of -caprolactone.

We classify Novikov᎐Poisson algebras whose Novikov algebras are simple with an idempotent element. Moreover, a class of simple Novikov algebras without idempotent elements is constructed through Novikov᎐Poisson algebras. Certain new simple Lie superalgebras induced by Novikov᎐Poisson algebras are introduced. ᮊ 1997 Academic Press

An efficient one-pot synthesis of 4,5,6-triaryl-3,4-dihydropyrimidin-2(1H)-ones via a three-component Biginelli-type condensation of aldehyde, 2-phenylacetophenone, and urea/thiourea in the presence of a catalytic amount of t-BuOK (20 mol %) is described. The reactions proceeded efficiently at 70 degrees C to afford the desired products in moderate to good yields. Detailed mechanistic study shows that the Biginelli-type reaction using urea and thiourea proceeds through two totally different pathways. Enone 5 and bis-urea 8 were highly suggested as respective reaction intermediates for reactions involving thiourea and urea as substrates.

We construct four new series of generalized simple Lie algebras of Cartan type, using the mixtures of grading operators and down-grading operators. Our results in this paper are further generalizations of those in Osborn's work (J. Algebra 185 (1996), 820-835).

A convenient method for the synthesis of lanthanide alkoxo complexes supported by a carbon-bridged bis(phenolate) ligand 2,2'-methylenebis(6-tert-butyl-4-methylphenoxo) (MBMP2-) is described. The reaction of (C5H5)3Nd with MBMPH2 in a 1:1 molar ratio in THF gave the bis(phenolato)lanthanide complex (C5H5)Nd(MBMP)(THF)2 (1) in a nearly quantitative yield. Complex 1 further reacted with 1 equiv of 2-propanol in THF to yield the bis(phenolato)lanthanide isopropoxide [(MBMP)2Nd(mu-OPr(i))(THF)2]2 (2) in high yield. Complex 2 can also be synthesized by the direct reaction of (C5H5)3Nd with MBMPH2 in a 1:1 molar ratio and then with 1 equiv of 2-propanol in situ in THF. Thus, the analogue bis(phenolato)lanthanide alkoxides [(MBMP)2Ln(mu-OR)(THF)2]2 [R = Pr(i), Ln = Yb (3); R = Me, Ln = Nd (4), Yb (5); R = CH2Ph, Ln = Nd (6), Yb (7)] were obtained by the reactions of (C5H5)3Ln (Ln = Nd, Yb) with MBMPH2 and then with 2-propanol, methanol, or benzyl alcohol, respectively. The ytterbium complex {[(MBMP)2Yb(THF)2]2(mu-OCH2Ph)(mu-OH)} (8) was also isolated as a byproduct. The single-crystal structural analyses of complexes 1-3 and 8 revealed that the coordination geometry around lanthanide metal can be best described as a distorted tetrahedron in complex 1 and as a distorted octahedron in complexes 2, 3, and 8. A O-H...Yb agostic interaction was observed in complex 8. Complexes 2-7 were shown to be efficient catalysts for the controlled polymerization of epsilon-caprolactone.

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